/*
 * Copyright (c) 2013, SRI International
 * All rights reserved.
 * Licensed under the The BSD 3-Clause License;
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at:
 * 
 * http://opensource.org/licenses/BSD-3-Clause
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 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
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 * Redistributions of source code must retain the above copyright
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 * Redistributions in binary form must reproduce the above copyright
 * notice, this list of conditions and the following disclaimer in the
 * documentation and/or other materials provided with the distribution.
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 * Neither the name of the aic-expresso nor the names of its
 * contributors may be used to endorse or promote products derived from
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 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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package com.sri.ai.grinder.library.equality.cardinality.direct.core;

import com.google.common.annotations.Beta;
import com.sri.ai.expresso.api.Expression;
import com.sri.ai.expresso.helper.Expressions;
import com.sri.ai.grinder.api.RewritingProcess;
import com.sri.ai.grinder.core.AbstractHierarchicalRewriter;
import com.sri.ai.grinder.helper.Trace;
import com.sri.ai.grinder.library.Equality;
import com.sri.ai.grinder.library.FunctorConstants;
import com.sri.ai.grinder.library.boole.ForAll;
import com.sri.ai.grinder.library.boole.ThereExists;
import com.sri.ai.grinder.library.equality.cardinality.CardinalityUtil;
import com.sri.ai.grinder.library.equality.cardinality.direct.CardinalityRewriter;

/**
 * Default implementation of R_top_quantifier_elimination(Qx F).
 * 
 * @author oreilly
 *
 */
@Beta
public class TopQuantifierElimination extends AbstractHierarchicalRewriter implements CardinalityRewriter {
	
	public TopQuantifierElimination() {
	}
	
	
	@Override
	public String getName() {
		return R_top_quantifier_elimination;
	}
	
	/**
	 * @see CardinalityRewriter#R_top_quantifier_elimination
	 */
	@Override
	public Expression rewriteAfterBookkeeping(Expression expression, RewritingProcess process) {
		Expression result = null;
		
		// Assert input arguments, Qx F
		CardinalityRewriter.Quantification quantification = null;
		Expression                         indexX         = null;
		Expression                         f              = null;
		if (ForAll.isForAll(expression)) {
			quantification = CardinalityRewriter.Quantification.FOR_ALL;
			indexX         = CardinalityUtil.getForAllIndex(expression);
			f              = ForAll.getBody(expression);
		} 
		else if (ThereExists.isThereExists(expression)) {
			quantification = CardinalityRewriter.Quantification.THERE_EXISTS;
			indexX         = CardinalityUtil.getThereExistsIndex(expression);
			f              = ThereExists.getBody(expression);
		} 
		else {
			throw new IllegalArgumentException("Invalid input argument expression, Qx F expected, where Q is a quantifier over x:"+expression);
		}
	
		Trace.log("F <- R_top_simplify(F)");
		f = process.rewrite(R_top_simplify, f);
		
		if (quantification == CardinalityRewriter.Quantification.FOR_ALL) {
			Trace.log("if Q is \"for all\"");
			Trace.log("    return R_simplify( R_card(|F|_x, Q) = |type(x)| )");
		} 
		else {
			Trace.log("if Q is \"there exists\"");
			Trace.log("    return R_simplify( R_card(|F|_x, Q) > 0)");
		}
		
		Expression cardinalityOfIndexedFormaulaF = CardinalityUtil.makeCardinalityOfIndexedFormulaExpression(f, indexX);
		Expression resultCard1                   = process.rewrite(R_card, CardinalityUtil.argForCardinalityWithQuantifierSpecifiedCall(cardinalityOfIndexedFormaulaF, quantification));
		
		if (quantification == CardinalityRewriter.Quantification.FOR_ALL) {
			Expression cardIndexX            = CardinalityUtil.makeCardinalityOfIndexExpressions(indexX);
			Expression resultCard1EqualCardX = Equality.make(resultCard1, cardIndexX);
			
			result = process.rewrite(R_simplify, resultCard1EqualCardX);
		} 
		else {
			Expression resultCard1NotEqual0 = Expressions.make(FunctorConstants.GREATER_THAN, resultCard1, Expressions.ZERO);
			
			result = process.rewrite(R_simplify, resultCard1NotEqual0);
		}
		
		return result;
	}
}
